1. The "cut" in a tournament is the elimination of, typically, the lower half of a stroke-play field at the midpoint of the tournament. In a four-day event, a cut might be made following the second round of play; the top half (typically) of the field continues on to the third and fourth rounds while the bottom half (typically) goes home.
But cuts can be made at any point in a tournament (following the first, second or third rounds), and sometimes more than one cut is made in a tournament. See Cut Line for more details, or check these FAQs for info on the cut in some specific tours or tournaments:
2. A "cut" is a type of golf shot in which the player induces a fade; a right-handed golfer makes the ball curve left-to-right in flight, while a left-hander creates a right-to-left ball flight.
In this meaning, "cut" can be a noun (the shot itself) or a verb ("He needs to cut this one around the tree limbs"). See also: Cut Shot.
3. "Cut" can also refer to the positioning of the cup on the green. For example, "the hole is cut on the front-left portion of the green." This meaning derives from hole-cutting tool used to remove the turf and sod where the cup is to be placed.